| Issue |
ESAIM: M2AN
Volume 49, Number 2, March-April 2015
|
|
|---|---|---|
| Page(s) | 395 - 420 | |
| DOI | https://doi.org/10.1051/m2an/2014038 | |
| Published online | 19 February 2015 | |
Parallelizing the Kolmogorov Fokker Planck Equation
Basque Center for Applied Mathematics Mazarredo 14, 48009 Bilbao, Spain.
lgerardo@bcamath.org; tbinh@bcamath.org
Received: 7 September 2013
Revised: 23 July 2014
We design two parallel schemes, based on Schwarz Waveform Relaxation (SWR) procedures, for the numerical solution of the Kolmogorov equation. The latter is a simplified version of the Fokker–Planck equation describing the time evolution of the probability density of the velocity of a particle. SWR procedures decompose the spatio-temporal computational domain into subdomains and solve (in parallel) subproblems, that are coupled through suitable conditions at the interfaces to recover the solution of the global problem. We consider coupling conditions of both Dirichlet (Classical SWR) and Robin (Optimized SWR) types. We prove well-posedeness of the schemes subproblems and convergence for the proposed algorithms. We corroborate our findings with some numerical tests.
Mathematics Subject Classification: 35K55 / 65M12 / 65M55
Key words: Domain decomposition / Schwarz waveform relaxation methods / optimized Schwarz / Kolmogorov equation / Fokker–Plank equation / kinetic equations
© EDP Sciences, SMAI, 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.